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Session Chair: Stefanie Reese, RWTH Aachen University Session Chair: Carolin Birk, Universität Duisburg-Essen
Location:Auditorium Wolfsburg
Presentations
Generalized Finite Difference Method for Compressible Flow Problems with Discontinuities
Tao Zhang, Rui Zhou
Beijing Institute of Technology, China, People's Republic of
In this study, the generalized finite difference method (GFDM) combined with an upwind scheme is applied to solve the compressible flow problem with discontinuities. GFDM is a meshless method developed in recent years. Based on Taylor series expansion and moving least squares (MLS) method, it converts the partial derivative into the linear summation of nodal values, avoiding complex grid generation and numerical integration. GFDM and the third order Runge-Kutta scheme are employed to discretize the Euler equations for compressible flow in space and time respectively. The upwind scheme in this paper is applied to overcome numerical oscillations when using high-order trial functions. Notably, the upwind scheme here is not based on the difference method but on Taylor series expansion and MLS. The present method avoids time-consuming mesh generation and numerical quadrature. Several typical numerical examples including one-dimensional and two-dimensional compressible flow problems are given to verify the effectiveness and accuracy of the proposed method. Numerical results also show that this method can accurately capture shockwaves.
